Question: Rewrite as a simplified fraction. ${2.\overline{45} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 245.4545...\\ 1x &= 2.4545...\end{align*}}$ Subtracting the two equations, we have: ${99x = 243}$ ${x = \dfrac{243}{99}} $ ${x = \dfrac{27}{11}} \text{or} {2 \dfrac{5}{11}}$